Simplify −−3√54 .

Question

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Answer 1

To simplify \(-\sqrt[3]{54}\), we can start by factoring 54 into its prime factors:

\[ 54 = 2 \times 27 = 2 \times 3^3. \]

Now, we can rewrite the cubic root:

\[ -\sqrt[3]{54} = -\sqrt[3]{2 \times 3^3}. \]

Using the property of cube roots, we can separate the factors:

\[ -\sqrt[3]{54} = -\sqrt[3]{2} \times \sqrt[3]{3^3}. \]

Since \(\sqrt[3]{3^3} = 3\), we have:

\[ -\sqrt[3]{54} = -\sqrt[3]{2} \times 3 = -3\sqrt[3]{2}. \]

Thus, the simplified form of \(-\sqrt[3]{54}\) is:

\[ -\sqrt[3]{54} = -3\sqrt[3]{2}. \]